August 14, 2008

The Omnipotence Paradox (or: Why Hackers are like God)

So much RSI has been induced by this conundrum over the years that it's almost a shame to bring it up again. But it's an important stumbling block so it needs to be spelled out. Essentially, the argument is a very simple reductio ad absurdum against the concept of an omnipotent entity, usually directed at the Judeo-Christian God. The way it works is simple:

God is omnipotent (meaning that he can do anything.)
God therefore must be able to conjure an act which He is incapable.
quod erat demonstrandum:
God is not omnipotent.

There is a derivate of the argument, specific to particular interpretations of the omnipotent being, particularly those which insist on this being being omnibenevolent and omniscient in addition to being omnipotent. This argument generally goes like this:

God is omnibenevolent (and therefore wills the abolition of pain and suffering)
God is omnipotent and omniscient (and therefore can prevent all pain and suffering)
There is pain and suffering.
quod erat demonstrandum:
God is either not: omnibenevolent, omniscient, omnipotent or some combination thereof.

Together, these two arguments make up the core of any argument against mainstream theism. Now, the first argument can be settled with a very obvious observation, that the ability to handicap oneself does not make one handicapped. And so, the notion that an omnipotent deity could handicap itself, does not make it any less omnipotent at this current moment. However, this observation fails to answer the second argument with any satisfaction and completely misses the core of the misunderstanding.

The core of this misunderstanding is pretty simple. Our words do not mean what we think they mean. Our problem , of course, is with the word 'omnipotent.' The colloquial understanding of the word is this:

- The ability to actualize any cognition.

That is, can do anything we can think of, regardless of any inherent contradiction, which in fact incorrect. The real meaning is more subtle. This is to be expected, seeing as the word is an import from Latin, A language which is usually more precise in modern times than English. Naturally, omnipotent comes from the Latin roots: 'Omni' and 'Potens,' meaning 'all' and 'power' respectively. When combined, they mean something akin to "power over all things." Thus omnipotence is a reference not to what the entity can do, per se, but what the entity has power over. Hence, a better understanding would go thus:

-Absolute control over all of reality, in whole and in part.

This definition, while superficially sounding very much the same as the previous definition, actually suggests a much different relationship between omnipotent entity and the rest of reality. In the former definition, the deity acted more like an abstract will, arbitrating existence from a purely idealistic standpoint. The second definition, however, establishes omnipotence as, not some kind of innate property of the omnipotent, but as a relationship of the omnipotent to reality.


Up to this point, this argument has been exposited before, many times. (Hence the RSI.) One can check Wikipedia for a good discussion of the issue in great philosophical depth. Normally at this point in the explanation, one uses some kind of analogy, and I'm no exception. However, my analogy will be a little different. Instead of Lewis's wonderfully eccentric painter, I've got a megalomaniac hacker (in the positive sense of the word).

You'll see how this works: A computer is a tool for automation and abstraction. It contains a world unto its own in which arbitrary sequences of boolean values are assigned meanings. All kinds of meanings mind you: meanings such as '4,' 'addition,' and 'kill neighbor,' are all valid. By merely mapping values to an underlying set of instructions and formats designed to hold any kind of information imaginable, one can literally simulate any kind of world. Freed from the constraints of physical matter, computers can simulate all kinds of worlds possessed of any kind of laws and with any variables set. With respect to these worlds, the creator, (in this instance a hacker,) is omnipotent.

Let's look at this omnipotence. A hacker can create a world which mirror our own:
(setf 'one 1)
(setf 'two 2)
(setf 'three 3)
(setf 'four 4)
(setf 'five 5)
So that the world's behavior mirrors our own:
(+ 'two 'two) => 4
Or he can create a world which is different:
(setf 'one 5)
(setf 'two 4)
(setf 'three 3)
(setf 'four 2)
(setf 'five 1)
And so create bizarre aberrations:
(+ 'two 'two) => 8
(+ 'five 'four) => 3
Or they can even change the rules at their most fundamental level:
(defun + (&rest rest)
(reduce #'- rest))
To remake reality in any arbitrary fashion desired:
(+ 2 2) => 0
Indeed, with the proper tools and knowhow, the hacker can even change the value of any variable, and redefine and function, at runtime. With respect to the little simulated computer people and their simulated computer world, he is god, and this is what we mean by omnipotent.

There are some things, however, that our hacker cannot do. He cannot, for example, make the simulation run faster than a certain point due to physical limitations of the computer. This doesn't affect his omnipotence however; he still has absolute control over the nature of his simulated world, this a limitation of the world in which he it a part. His control still holds, but it seems that there is a sort of meta law to which his law must conform. The hacker may create a world that is subject to any rules he chooses, but he may not in doing so violate any laws to which he himself is subject.

We can thus apply this perception of omnipotence to a supposedly omnipotent entity: The great hacker who created the great simulation in which we are but objects. He controls the fabric of our universe, but cannot violate the fabric of his own. We thus see how omnipotence is not impossible, just over ambitiously defined.

But, we haven't really gained anything from this. We've removed one of the difficulties in approaching the concept of an omnipotent being, but at the same time, we've removed the chief advantage: that an omnipotent being provides a Occamian explanation for reality (this, in fact is very similar to the first application of his so called razor.) That is, it is easiest to explain all of reality as coming from a single principle, and this principle is most easily described as some sort of demiurge, which would necessarily be omnipotent in the manner described by this definition.

Fortunately, this problem is simple to escape. Even if we assumed the hacker had a magical computer which was freed of all physical limitations and he himself was freed all physical limits as well, there would still be limits on his actions. Those come not from any limits placed on the machine or scientist externally but those stemming from the scientist himself. Even if we were to pull out all of the stops, he would still be limited by his own imagination. In this hypothetical, the hacker could define function '+' such that it meant division, multiplication, addition, and subtraction all at the same time and in exactly the same context without distinction, except that that concept would be meaningless to him. He himself is unsure of what that would mean.

Does he mean?:
(defun + '((lambda (&rest rest) (reduce #'/ rest))
(lambda (&rest rest) (reduce #'* rest))
(lambda (&rest rest) (reduce #'+ rest))
(lambda (&rest rest) (reduce #'- rest))))
Or does he mean?:
(defun + (&rest rest) (reduce #'/ rest))
(defun + (&rest rest) (reduce #'* rest))
(defun + (&rest rest) (reduce #'+ rest))
(defun + (&rest rest) (reduce #'- rest))
In fact, there is no way to express it because the scientist, being human, has no conception of what something to be multiple things at the same time without distinction would mean.

In the same vein, an omnipotent demiurge is bound by its own nature. Anthropomorphizing it, it is bound by its goals, logic, thoughts, and imagination. If creating a simulation of a certain nature necessarily implies that that simulation posses a certain attribute which necessarily leads to a certain consequence, then the demiurge simply cannot both create that simulation and avoid that consequence. A hacker simply cannot create a process that both unceasingly conses and unceasingly accesses. It is not just physically impossible, but non-nonsensical.

And so, we come to the concept of 'god.' He is a hacker, living in a world where there is nothing but himself, and has chosen to create a simulation, (necessarily) of himself. This simulation, in order to be true to life, must include things like 'wills' and 'intellects,' and so, even though the great hacker in the sky is omnipotent, he must sacrifice a certain amount of control lest he contradict his own intent. To create a willful creature whose actions are predetermined is a contradiction. This concept, just like the '+' function mentioned earlier, has no meaning and our omnipotent hacker, like the any regular one, cannot do something which has no meaning.

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